Machines for packing envelopes are known. For example, U.S. Pat. No. 3,562,775 (Mullins) discloses such an apparatus in which cartons or cardboard boxes are placed from above onto standing stacked envelopes. The cartons, with their contents, then slide downwardly along an inclined plane and are braked against a stop in such a manner that they tip over and finally come to rest on a conveyor belt with the floor or bottom of the carton facing downwardly and the opening of the carton facing upwardly. In the prior art apparatus, the cartons are supplied in a direction perpendicular to the transport direction of the envelopes which are standing in stacks, and the cartons along with their content envelopes are further transported along the inclined plane to the conveyor belt in a direction perpendicular to or across the original transport direction of the envelopes. Such an arrangement or apparatus requires that sufficient space is available for the perpendicularly directed transport of the empty and the full cartons. Often, however, the required space is not available.